Weighted sparsity-based denoising for extracting incipient fault in rolling bearing

Given that the incipient fault is too weak for extraction, a novel approach that is based on sparse optimization is proposed for incipient fault diagnosis. The proposed optimization method consists of three steps: First, autocorrelation analysis is utilized to filter broadband random noise. Then, the weighted sparsity-based denoising method is proposed to extract periodic impulses. The prior knowledge that periodic impulses are sparse is used to constitute a penalty term; thus a novel weighted sparse optimization model is established. The majorization-minimization method is used to solve the optimization model. The high-pass filter in quadratic fidelity term is constructed by a Butterworth filter based on banded matrices, thus effectively improving computational efficiency. Lastly, the interval of periodic impulses, which corresponds to the fault frequency of rolling bearing, is obtained. Moreover, simulation and experimental results show that the proposed approach can successfully extract fault features from the signals of low signal to noise ratio.